2018-05-25T00:14:00Zhttp://ijmc.kashanu.ac.ir/?_action=export&rf=summon&issue=59542017-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-6489201784Borderenergetic graphs of order 12B.FurtulaI.GutmanA graph G of order n is said to be borderenergetic if its energy is equal to 2n-2 and if G differs from the complete graph Kn. The first such graph was discovered in 2001, but their systematic study started only in 2015. Until now, the number of borderenergetic graphs of order n was determined for nGraph energyBorderenergetic graphSpectrum (of graph)20171201339343http://ijmc.kashanu.ac.ir/article_49788_e4fd7626f4f5ccd491b2376fc1ba6d33.pdf2017-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-6489201784A numerical study of fractional order reverse osmosis desalination model using Legendre wavelet approximationO.BelhamitiB.AbsarThe purpose of this study is to develop a new approach in modeling and simulation of a reverse osmosis desalination system by using fractional differential equations. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. Examples are developed to illustrate the fractional differential technique and to highlight the broad applicability and the efficiency of this method. The fractional derivative is described in the Caputo sense.Reverse osmosis desalination systemLegendre wavelet methodDQL- techniqueCaputo fractional derivative20171201345364http://ijmc.kashanu.ac.ir/article_48032_ff48681a45a60de0429bac163d8c4c22.pdf2017-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-6489201784Solving time-fractional chemical engineering equations by modified variational iteration method as fixed point iteration methodA.HaghbinH.JafariThe variational iteration method(VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The obtained approximate solutions are compared with the numerical results in the literature to show the applicability, efficiency and accuracy of the method.Fractional differential equationsVariational iteration methodFixed point theoryChemical reactor20171201365375http://ijmc.kashanu.ac.ir/article_45351_7ad4e59b4cdb4132de2c3a8367a50a90.pdf2017-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-6489201784The ratio and product of the multiplicative Zagreb‎ ‎indicesR.Kazemi‎The first multiplicative Zagreb index $Pi_1(G)$ is equal to the‎ ‎product of squares of the degree of the vertices and the second‎ ‎multiplicative Zagreb index $Pi_2(G)$ is equal to the product of‎ ‎the products of the degree of pairs of adjacent vertices of the‎ ‎underlying molecular graphs $G$‎. ‎Also‎, ‎the multiplicative sum Zagreb index $Pi_3(G)$ is equal to the product of‎ ‎the sums of the degree of pairs of adjacent vertices of $G$‎. ‎In‎ ‎this paper‎, ‎we introduce a new version of the multiplicative sum‎ ‎Zagreb index and study the moments of the ratio and product of ‎all above‎ indices in a randomly chosen molecular graph with tree structure of order $n$. ‏Also, a ‎supermartingale is introduced by ‎‎Doob's supermartingale‎ ‎inequality.Molecular graph with tree structure‎, Multiplicative Zagreb indicesMomentsDoob&#039;s supermartingale‎ ‎inequality‎20171201377390http://ijmc.kashanu.ac.ir/article_45116_bba187473ad5bfb18a6a43340e77aeed.pdf2017-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-6489201784Extermal trees with respect to some versions of Zagreb indices via majorizationM.EliasiA.GhalavandThe aim of this paper is using the majorization technique to identify the classes of trees with extermal (minimal or maximal) value of some topological indices, among all trees of order n ≥ 12majorizationGeneral first Zagreb indexMultiplicative Zagreb indices20171201391401http://ijmc.kashanu.ac.ir/article_48642_8ce4604ddc78e89ae0e39ca4005451db.pdf2017-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-6489201784The uniqueness theorem for inverse nodal problems with a chemical potentialS.MosazadehIn this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.Boundary Value problemInverse Nodal problemEigenvaluesNodal points20171201403411http://ijmc.kashanu.ac.ir/article_39228_74fccfc43fcca7799b30709c291e6cdc.pdf2017-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-6489201784Numerical modeling for nonlinear biochemical reaction networksZ. A.ZafarK.RehanM.MushtaqM.RafiqNowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A NSFD model has been constructed for the biochemical reaction problem and numerical experiments are performed for different values of discretization parameter ‘h’. The results are compared with the well-known numerical scheme, i.e. RK4. Unlike RK4 which fails for large time steps, the developed scheme gives results that converge to true steady states for any time step used.Michaelis-Menten modelNSFD MethodRK4 method20171201413423http://ijmc.kashanu.ac.ir/article_50016_11567eff2592ac019bf3417a8b52b650.pdf2017-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-6489201784Numerical solution of gas solution in a fluid‎: ‎fractional derivative modelS.Esmaeili‎A computational technique for solution of mathematical model of gas solution in a fluid is presented‎. ‎This model describes the change of mass of the gas volume due to diffusion through the contact surface‎. ‎An appropriate representation of the solution based on the M"{u}ntz polynomials reduces its numerical treatment to the solution of a linear system of algebraic equations‎. ‎Numerical examples are given and discussed to illustrate the effectiveness of the proposed approach‎.‎Fractional derivatives‎‎Gas ‎solution‎M"{u}ntz polynomials‎‎Gaussian quadrature‎‎Collocation method‎20171201425437http://ijmc.kashanu.ac.ir/article_50034_5c2f08ce942057f910e8a78543fd8011.pdf